Adaptive quadrature for sharply spiked integrands

Authors:
Samarth Agarwal;Michael Povolotskyi;Tillmann Kubis;Gerhard Klimeck
Affiliations:
Department of Physics, Purdue University, West Lafayette, USA 47907;School of Electrical and Computer Engineering, Purdue University, West Lafayette, USA 47907;School of Electrical and Computer Engineering, Purdue University, West Lafayette, USA 47907;School of Electrical and Computer Engineering, Purdue University, West Lafayette, USA 47907
Venue:
Journal of Computational Electronics
Year:
2010

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Algorithm 145: Adaptive numerical integration by Simpson's rule

Communications of the ACM
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

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Abstract

A new adaptive quadrature algorithm that places a greater emphasis on cost reduction while still maintaining an acceptable accuracy is demonstrated. The different needs of science and engineering applications are highlighted as the existing algorithms are shown to be inadequate. The performance of the new algorithm is compared with the well known adaptive Simpson, Gauss-Lobatto and Gauss-Kronrod methods. Finally, scenarios where the proposed algorithm outperforms the existing ones are discussed.